Resonance states completeness for relativistic particle on a sphere with two semi-infinite lines attached
The paper is devoted to resonances playing an important role in direct and inverse scattering problems. A model of a relativistic particle on hybrid manifold consisting of a sphere with two semi-infinite wires attached is considered. The model is based on the theory of self-adjoint extensions of sym...
| Main Authors: | , , |
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| Format: | Article |
| Language: | English |
| Published: |
Elsevier
2020-01-01
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| Series: | Journal of King Saud University: Science |
| Online Access: | http://www.sciencedirect.com/science/article/pii/S1018364718307080 |
| Summary: | The paper is devoted to resonances playing an important role in direct and inverse scattering problems. A model of a relativistic particle on hybrid manifold consisting of a sphere with two semi-infinite wires attached is considered. The model is based on the theory of self-adjoint extensions of symmetric operators. Completeness of resonance states in the space of square integrable functions on the sphere is proved. The proof uses the relation between the completeness and the factorization of the characteristic function in Sz.-Nagy functional model. Keywords: Scattering, Resonance, Hybrid manifold, Dirac operator, MSC 2010: 47B38, 47E05 |
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| ISSN: | 1018-3647 |